Abstract
In this paper, the topology optimization of continuum structures with design-dependent loads is studied with a gradient-free topology optimization method in combination with adaptive body-fitted finite element mesh. The material-field series-expansion (MFSE) model represents the structural topology using a bounded material field with specified spatial correlation and provides a crisp structural boundary description. This feature makes it convenient to identify the loading surface for the application of the design-dependent boundary loads and to generate a body-fitted mesh for structural analysis. Using the dimension reduction technique, the number of design variables is significantly decreased, which enables the use of an efficient Kriging-based algorithm to solve the topology optimization problem. The effectiveness of the proposed method is demonstrated using several numerical examples, among which a design problem with geometry and contact nonlinearity is included.
Highlights
During the past three decades, topology optimization has been widely applied to determine the optimal material distribution of various structural and multidisciplinary design problems [1,2,3,4,5,6,7]
Compared with structural topology optimization with invariant loads, the main feature of the optimization problems with design-dependent loads is that the load boundaries keep evolving during the optimization procedures
According to the load direction, design-dependent loads can be generally classified into two categories: (i) the load direction is always perpendicular to the loading surface, such as the fluid pressure load on structures in hydrostatics problems; (ii) the load direction is fixed, such as the soil pressure load on civil structures
Summary
During the past three decades, topology optimization has been widely applied to determine the optimal material distribution of various structural and multidisciplinary design problems [1,2,3,4,5,6,7]. A general gradientfree topology optimization framework that combines the material-field series-expansion (MFSE) model [36,37,38] and an adaptive body-fitted finite element mesh is proposed. The topology optimization aimed at minimizing the compliance of a structure subjected to design-dependent pressure loads with given material usage, and Symmetry 2021, 13, 1976. The topology optimization aimed at minimizing the compliance of a structure subjected to design-dependent pressure loads with given material usage, and the formulation is as follows: find χ min C = P(χ)Tu(χ) s.t. K(χ)u = P(χ). Topology Optimization Based on Material-Field Series Expansion Model and Adaptive Body-Fitted Mesh
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